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A generalization of Anderson's theorem on unimodal functions

Author: Somesh Das Gupta
Journal: Proc. Amer. Math. Soc. 60 (1976), 85-91
MSC: Primary 26A87; Secondary 52A40
MathSciNet review: 0425050
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Abstract: Anderson (1955) gave a definition of a unimodal function on $ {R^n}$ and obtained an inequality for integrals of a symmetric unimodal function over translates of a symmetric convex set. Anderson's assumptions, especially the role of unimodality, are critically examined and generalizations of his inequality are obtained in different directions. It is shown that a marginal function of a unimodal function (even if it is symmetric) need not be unimodal.

References [Enhancements On Off] (What's this?)

  • [T] W. Anderson (1955), The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6, 170-176. MR 16, 1005. MR 0069229 (16:1005a)
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Keywords: Unimodal function, convex set, invariance, marginal function, inequalities
Article copyright: © Copyright 1976 American Mathematical Society

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